Pełnotekstowe zasoby PLDML oraz innych baz dziedzinowych są już dostępne w nowej Bibliotece Nauki.
Zapraszamy na https://bibliotekanauki.pl

Ograniczanie wyników

Czasopisma help

  1. 3 Acta Arithmetica

Autorzy help

  1. 4 Ballot C.

  2. 2 Luca F.

Lata help

  1. 2 2013

  2. 1 2007

  3. 1 1999

Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last

Wyniki wyszukiwania

help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available remote

Lucas sequences with cyclotomic root field

100%
Ballot C.
Instytut Matematyczny Polskiej Akademii Nauk
EN
A pair of Lucas sequences Uₙ = (αⁿ-βⁿ)/(α-β) and Vₙ = αⁿ + βⁿ is famously associated with each polynomial x² - Px + Q ∈ ℤ[x] with roots α and β. It is the purpose of this paper to show that when the root field of x² - Px + Q is either ℚ(i), or ℚ(ω), where $ω = e^{2πi/6}$, there are respectively two and four other second-order integral recurring sequences of characteristic polynomial x² - Px + Q that are of the same kinship as the U and V Lucas sequences. These are, when ℚ(α,β) = ℚ(i), the G and the H sequences with Gₙ = [(1-i)αⁿ + (1+i)α̅ⁿ]/2, Hₙ = [(1+i)αⁿ + (1-i)α̅ⁿ]/2, and, when ℚ(α,β) = ℚ(ω), the S, T, Y and Z sequences given by Sₙ = (ωαⁿ - ω̅α̅ⁿ)/√(-3), Tₙ = (ω²αⁿ - ω̅²α̅ⁿ)/√(-3), Yₙ = ω̅αⁿ + ωα̅ⁿ, Zₙ = ωαⁿ + ω̅α̅ⁿ, where α̅ = β and $ω̅ = e^{-2πi/6}$. Several themes of the theory of Lucas sequences have been selected and studied to support the claim that the six sequences G, H, S, T, Y and Z ought to be viewed as Lucas sequences.
2
Content available remote

Strong arithmetic properties of the integral solutions of X³ + DY³ + D²Z³ - 3DXYZ = 1, where D = M³ ± 1, M ∈ ℤ*

96%
Ballot C.
Acta Arithmetica
|
1999
|
tom 89
|
nr 3
259-277
3
Content available remote

On the equation x² + dy² = Fₙ

61%
Ballot C., Luca F.
Acta Arithmetica
|
2007
|
tom 127
|
nr 2
145-155
4
Content available remote

On the sumset of the primes and a linear recurrence

61%
Ballot C., Luca F.
Acta Arithmetica
|
2013
|
tom 161
|
nr 1
33-46
EN
Romanoff (1934) showed that integers that are the sum of a prime and a power of 2 have positive lower asymptotic density in the positive integers. We adapt his method by showing more generally the existence of a positive lower asymptotic density for integers that are the sum of a prime and a term of a given nonconstant nondegenerate integral linear recurrence with separable characteristic polynomial.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.